Data Visualization for Kansei Analysis

Abstract

Kansei data are multi-dimensional data. It is difficult for an analyzer to interpret data whose dimensionality is higher than three because his/her vision is used only to one -- three dimensions. Visualization by reducing the dimensionality of Kansei data to less than or equal to three dimensions could help the analyzer to understand the data. For an effective visualization, definition of distances between data is important. For the definition, axes that form a space of Kansei data should be determined first. The choice could be questions or objects. A questionnaire uses several objects and many questions. Respondents are asked to answer each question one by one by marking on a rating scale. Questions are usually used as axes for multivariate analysis. Objects are another choice for the axes. By changing our viewpoint from different axes, new relationships between questions/objects could be found. One of the most popular visualization methods is PCA (Principal Component Analysis). By applying PCA to questionnaire data on question axes, relationships between objects can be visualized. If the method is applied to the data on object axes, relationships between questions can be seen. The distance used in PCA is usually Euclidean distance. If some features can be extracted by a nonlinear transformation from original data, distances can be defined between the features. Kernel PCA[1] can be applied and kernel trick would work for dealing with multi-dimensional features. MDS (Multi-Dimensional Scaling)[2][3] is also an effective visualization method. This method is to reduce the dimensionality of data while preserving the distances or dissimilarities between data in the original space. The weights on the differences between the distances in the visualized space and those in the original hyper-space make MDS a flexible tool for the visualization. These weights can be set to determine distances to be preserved or ignored. In exploratory visual data analysis, interactive manifold unfolding can be carried out by setting these weights. ISOMAP[4] is an extension of MDS in which Euclidean distance is replaced with geodesic distance. Kansei data on manifold embedded in a hyper-dimensional space could be measured by their geodesic, or shortest path, distances and the manifold can be unfolded and visualized.